Politicians have access to the studies showing that such infrastructure when built has the desired effect, and studies showing that the number one reason people don't cycle more is that they feel unsafe riding among traffic, regardless of helmets. Governments have the job of providing infrastructure to enable cities to function, and in many cases better bicycle infrastructure is the cheapest way to achieve it.
There also studies about how car on-ramps can be built, how sidewalks should be routed, how schools should be organized, etc. etc.
And money has to be split between all those things. A government has to provide for its people’s needs and if its people show no interest in cycling, some other more pressing problem is going to take priority
They ignore it as long as there is a vocal contingent of people against cycling infrastructure because of cost or because it may create a slight disruption to a car.
Some do, sure. But thankfully at least where I live governments (both state and local-level) have seen the benefits of improving cycling infrastructure and are continuing to do so. A good many car drivers are quite happy to not have to share roads with bikes too! Well-built cycling infrastructure makes roads better for all users, esp. if it can reduce the number of unnecessary car trips.
